110 ❯ STEP 4. Review the Knowledge You Need to Score High
KEY IDEAWe could work this into the combined gas law, but more commonly the amount of
gas is related to the other physical properties through another relationship that Avogadro
developed:
1 mol of any gas occupies 22.4 L at STP
[standard temperature and pressure of 0°C (273 K) and 1 atm]
The combined gas law and Avogadro’s relationship can then be combined into the ideal
gas equation, which incorporates the pressure, volume, temperature, and amount relation-
ships of a gas.Ideal Gas Equation
The ideal gas equation has the mathematical form of PV = nRT, where:
P = pressure of the gas in atm, torr, mm Hg, Pa, etc.
V = volume of the gas in L, mL, etc.
n = number of moles of gas
R = ideal gas constant: 0.0821 L·atm/K·mol
T = Kelvin temperature
This is the value for R if the volume is expressed in liters, the pressure in atmospheres,
and the temperature in Kelvin (naturally). You could calculate another ideal gas constant
based on different units of pressure and volume, but the simplest thing to do is to use the
0.0821 and convert the given volume to liters and the pressure to atm. And remember that
you must express the temperature in kelvin.
Let’s see how we might use the ideal gas equation. Suppose you want to know what
volume 20.0 g of hydrogen gas would occupy at 27°C and 0.950 atm. You have the pres-
sure in atm, you can get the temperature in kelvin (27°C + 273 = 300. K), but you will
need to convert the grams of hydrogen gas to moles of hydrogen gas before you can use the
ideal gas equation. Also, remember that hydrogen gas is diatomic, H 2.
First, you’ll convert the 20.0 g to moles:
(20.0 g/l) × (1 mol H 2 /2.016 g) = 9.921 mol H 2
(We’re not worried about significant figures at this point, since this is an intermediate
calculation.)
Now you can solve the ideal gas equation for the unknown quantity, the volume:
PV = nRT
V = nRT/P
Finally, plug in the numerical values for the different known quantities:V = (9.921 mol)(0.0821 L atm/K mol) (300. K)/0.950 atm
V = 257 L
Is the answer reasonable? You have almost 10 mol of gas. It would occupy about 224 L
at STP (10 mol × 22.4 L/mol) by Avogadro’s relationship. The pressure is slightly less
than standard pressure of 1 atm, which would tend to increase the volume (Boyle’s law),
and temperature is greater than standard temperature of 0°C, which would also increase
the volume (Charles’s law). So you might expect a volume greater than 224 L, and that is
exactly what you found.
Remember, the final thing you do when working any type of chemistry problem is
answer this question: Is the answer reasonable?
KEY IDEA